Skip to main content
SpringerLink
Log in

The product structure of finitely presented dynamical systems

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

We consider finitely presented systems, which were introduced by Fried, and examine the circumstances under which these systems have canonical coordinates. We give necessary and sufficient conditions for their existence in a combinatorial way.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. Baladi,Gibbs and equilibrium states for finitely presented dynamical systems, J. Stat. Phys., to appear.

  2. R. Bowen,On Axiom A Diffeomorphisms, CBMS Reg. Conf. 35, American Mathematical Society, Providence, 1978.

    MATH  Google Scholar 

  3. R. Bowen,Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Math.470, Springer, Berlin, 1975.

    MATH  Google Scholar 

  4. R. Bowen,Topological entropy and Axiom A, Proc. Am. Math. Soc.14 (1971), 23–42.

    Google Scholar 

  5. E. Coven and M. Paul,Sofic systems, Isr. J. Math.20 (1975), 165–177.

    Article  MATH  MathSciNet  Google Scholar 

  6. M. Dateyama,Homeomorphisms with Markov partitions, Osaka J. Math.26 (1989), 411–428.

    MATH  MathSciNet  Google Scholar 

  7. A. Fathi,Expansiveness, hyperbolicity and Hausdorff dimension, Commun. Math. Phys.126 (1989), 249–262.

    Article  MATH  MathSciNet  Google Scholar 

  8. D. Fried,Métriques naturelles sur les espaces de Smale, C.R. Acad. Sci. Paris297 (1983), 77–79.

    MATH  MathSciNet  Google Scholar 

  9. D. Fried,Finitely presented dynamical systems, Ergodic Theory & Dynamic Systems7 (1987), 489–507.

    MATH  MathSciNet  Google Scholar 

  10. J. Kelly,General Topology, Van Nostrand, Princeton, NJ, 1955.

    Google Scholar 

  11. A. Manning,Axiom A diffeomorphisms have rational zeta functions, Bull. London Math. Soc.3 (1971), 215–220.

    Article  MATH  MathSciNet  Google Scholar 

  12. D. Ruelle,Thermodynamic Formalism, Addison Wesley, Reading, Mass., 1978.

    MATH  Google Scholar 

  13. S. Smale,Differential dynamical systems, Bull. Am. Math. Soc.73 (1967), 747–817.

    Article  MathSciNet  Google Scholar 

  14. P. Walters,On the pseudo orbit tracing property and its relationship to stability, Lecture Notes in Math.668, Springer, Berlin, 1978, pp. 231–244.

    Google Scholar 

  15. B. Weiss,Subshifts of finite type and sofic systems, Monatsh. Math.77 (1973), 462–474.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Southern California, 90089, Los Angeles, CA, USA

    Nicolai T. A. Haydn

Authors
  1. Nicolai T. A. Haydn
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Haydn, N.T.A. The product structure of finitely presented dynamical systems. Israel J. Math. 73, 343–356 (1991). https://doi.org/10.1007/BF02773846

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02773846

Keywords

Search

Navigation